Your bird should not have a problem with the cold. They pull their neck in and hunker down to cover their feet and stay warm. My roosters do well even when it is below zero. Make sure they have plenty of corn to eat and a full crop when they go to roost; that is when it gets cold ( below zero). As long as they have plenty of food and water, they will be just fine. Birds with single combs will suffer frost bite on their combs, that is the way it is- unless you put in a heat lamp. Even if they do suffer frost bite, the dead comb will fall off with no harm to the bird.
Tim
Tim